Why doesn't the circle have a face like the plane?
By default blender doesn't fill the circle. There are two types of fillings for circle. You can do it either manually or select it from the pop-up menu that appears when you add in the circle. The two types of filling are:-
1. Ngon-
In this type of filling it'll just add in a single face.
You can manually make it by switching to Edit Mode, select all vertices and press F or select it as shown in the image: The disadvantage of ngon filling is that you wont be able to add in loopcuts .

2. Triangle Fan
In this filling, there is a center vertex which is connected with all other outer vertices.
In this type of filling you can easily add in circular loopcuts to add more geometry if needed.
You can manually model it by selecting all vertices in edit mode with A fill it usually with  F and navigate to Face &gt; Poke Faces OR select it from the pop-up menu.

Selecting between this two fillings depend on when and where you use it.